In which stage of development does the child undergo astoundingly rapid change, and increase some 20 times in size, including dramatic changes in proportion and weight?

Fetal.

Explanation:

The fusion of the male and female gamete leads to the formation of zygote. The zygote growth further in the womb of the female. The human being gestation period is nine months.

The fetal development starts after zygote formation and till the birth of a baby. The fetus grows regularly in size and development of the body organs completed in the nine months. The weight and size increase rapidly and baby face well developed at the 14 week of pregnancy. Finger nails are well developed around 40 weeks of pregnancy.

Thus, the correct answer is fetal.